Determine the function satisfying `f^2(x+y)=f^2(x)+f^2(y)AAx ,y in Rdot`

Let a real valued function f satisfy f(x + y) = f(x)f(y)AA x, y in R and f(0)!=0 Then g(x)=f(x)/(1+[f(x)]^2) is

Let f :R to R be a differentiable function satisfying: f (xy) =(f(x))/(y)+f(y)/(x) AAx, y in R ^(+) also f (1)=0,f '(1) =1 find lim _(x to e) [(1)/(f (x))] (where [.] denotes greatest integer function).

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

If f(x) is a function satisfying f(x)-f(y)=(y^y)/(x^x)f((x^x)/(y^y))AAx , y in R^*"and"f^(prime)(1)=1 , then find f(x)

Let 'f' be a fifferentiable real valued function satisfying f (x+2y) =f (x) +f (2y) + 6xy (x+2y) AA x, y in R. Then f ' (0), f" (1), f'(2)….. are in

Let f be a real valued function satisfying f(x+y)=f(x)f(y) for all x, y in R such that f(1)=2 . Then , sum_(k=1)^(n) f(k)=

Let f be a real valued function satisfying f(x+y)=f(x)+f(y) for all x, y in R and f(1)=2 . Then sum_(k=1)^(n)f(k)=

Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA , x,y in R, y!=0 and f(1)!=0 , f'(1)=3 then

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to